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Browse All Reviews > Mathematics Of Computing (G) > Numerical Analysis (G.1) > Roots Of Nonlinear Equations (G.1.5) > Polynomials, Methods For (G.1.5...)
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1-10 of 11
Reviews about "Polynomials, Methods For (G.1.5...)":
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 Computing real roots of real polynomials
Sagraloff M., Mehlhorn K. Journal of Symbolic Computation 73(C): 46-86, 2016. Type: Article
The computation of roots of a univariate polynomial is the most classical task in computational algebra. Since this problem arises in very many applications, plenty of techniques for its solution have been proposed. In this paper, Sagr...
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Dec 1 2015 |
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Algorithm 801: POLSYS_PLP: a partitioned linear product homotopy code for solving polynomial systems of equations
Wise S., Sommese A., Watson L. ACM Transactions on Mathematical Software 26(1): 176-200, 2000. Type: Article
The problem of solving large systems of polynomial equations arises in many application areas and poses difficult mathematical questions and computational challenges. This paper critically reviews the literature of the past two decades...
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Jun 1 2000 |
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Halley-like method with corrections for the inclusion of polynomial zeros
Petković M. Computing 62(1): 69-88, 1999. Type: Article
Iteration methods based on Halley’s method for finding zeros ofpolynomial functions are presented. The idea is to use a complex variantof interval arithmetic, called circular complex arithmetic. Rules forthe basic arithmetic ...
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Oct 1 1999 |
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Detection and validation of clusters of polynomial zeros
Hribernig V., Stetter H. (ed) Journal of Symbolic Computation 24(6): 667-681, 1997. Type: Article
If some or all of the coefficients of a polynomial are known only to a specified accuracy, the concept of a multiple zero is meaningless, since an arbitrarily small change in the coefficients leads to the disintegration of an ...
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Jun 1 1998 |
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Improved techniques for factoring univariate polynomials
Collins G. (ed), Encarnación M. Journal of Symbolic Computation 21(3): 313-327, 1996. Type: Article
The main part of this paper describes extensions to the work of Wang [1] and Miola and Yun [2] on the derivation of integer factors for univariate polynomials. A new algorithm is derived, and its performance is compared to that of prev...
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Jul 1 1997 |
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Greatest factorial factorization and symbolic summation
Paule P. (ed) Journal of Symbolic Computation 20(3): 235-268, 1995. Type: Article
In 1873, Charles Hermite noted that the integration of rational functions F ( x ) &slash; f ( x ) can be reduced to that of functions whose denominator is square-free by a formula F ( x ) &slash; f (...
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Apr 1 1997 |
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The mathematical basis and a prototype implementation of a new polynomial rootfinder with quadratic convergence
Hull T., Mathon R. (ed) ACM Transactions on Mathematical Software 22(3): 261-280, 1996. Type: Article
A practical algorithm for simultaneous computation of all of the roots of a complex polynomial P ( z ) = σ ci z i is the subject of this paper. The algorithm is based on the Weierstra...
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Apr 1 1997 |
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Multipolynomial resultant algorithms
Manocha D., Canny J. Journal of Symbolic Computation 15(2): 99-122, 1993. Type: Article
The authors point out that classical elimination theory as summarized in Macaulay [1] requires the computation of large nonnumerical determinants, a task outside the capabilities of today’s symbolic computation software. Sinc...
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Feb 1 1996 |
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On generalized Newton algorithms
Malajovich G. Theoretical Computer Science 133(1): 65-84, 1994. Type: Article
Shub and Smale [1] used theorems on the quadratic convergence of Newton’s method to develop a theory of global complexity for the solution of systems of polynomial equations f k ( z ) = 0 , k = 1 ,..., n ,...
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Jun 1 1995 |
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A heuristic irreducibility test for univariate polynomials
Monagan M. Journal of Symbolic Computation 13(1): 47-57, 1992. Type: Article
The aim of this paper is to present an irreducibility criterion for univariate polynomials with integer coefficients. The method is based on the fact that, if the evaluation of the polynomial f at a well-chosen int...
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Apr 1 1993 |
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